Incest DOES suck. Now Japan doesn't consider cousins to be incest. But there is actually NO good reason these particular two I speak of should be together. He's bad for her and she's terrible for him. It's just a horrible, bad bad ship.

Maybe this case is really bad, I don't dispute that, as I haven't read the manga.
But are you sure they don't consider cousin marriage to be incest? I remember there was a married couple of cousins in one of the "Detective Conan" cases and they were looked upon as strange, the main characters were surprised they were allowed to marry.